Method and apparatus for time-free processing of GPS signals

ABSTRACT

A method and apparatus for computing GPS receiver position without using absolute time information transmitted by the satellite or by an alternative source of timing available at the GPS receiver. The GPS receiver is contained in an integrated receiver that also includes a wireless communication transceiver, but does not have access to an accurate source of absolute time information. The wireless transceiver communicates through a wireless network to a server. The GPS receiver measures satellite pseudoranges and uses the wireless communication transceiver to send the pseudoranges to the server. The server fits the pseudoranges to a mathematical model in which the GPS receiver position and the absolute time are unknown parameters. The server then computes a position and absolute time that best fit the model, thus yielding the correct position for the GPS receiver, and the absolute time at which the pseudorange measurements were made.

BACKGROUND OF THE DISCLOSURE

1. Field of the Invention

The invention relates to satellite-based position location and, moreparticularly, the invention relates to a method and apparatus fortime-free processing of global positioning system (GPS) signals.

2. Description of the Background Art

Global Positioning System (GPS) receivers normally determine theirposition by computing time delays between transmission and reception ofsignals transmitted from satellites and received by the receiver on ornear the surface of the earth. The time delays multiplied by the speedof light provides the distance from the receiver to each of thesatellites that are in view of the receiver. The GPS satellites transmitto the receivers satellite-positioning data, so called “ephemeris” data.In addition to the ephemeris data, the satellites transmit to thereceiver absolute time information associated with the satellite signal,i.e., the absolute time signal is sent as a second of the week signal.This absolute time signal allows the receiver to unambiguously determinea time tag for when each received signal was transmitted by eachsatellite. By knowing the exact time of transmission of each of thesignals, the receiver uses the ephemeris data to calculate where eachsatellite was when it transmitted a signal. Finally, the receivercombines the knowledge of satellite positions with the computeddistances to the satellites to compute the receiver position.

The process of searching for and acquiring GPS signals, and reading theephemeris and related data, including absolute time, for a multiplicityof satellites is time consuming and introduces unacceptable delays incomputing the receiver position. In addition, in many situations, theremay be blockage of the satellite signals. In these cases the receivedsignal level can be too low to demodulate and derive the satellite datawithout error. However, in these degraded signal situations, thereceiver is capable of tracking the satellite signals, and measuringtime delays (and hence distance), if an external source of ephemeris andabsolute time is available.

Several innovations have been made to provide “GPS Aiding” that consistsof external sources of ephemeris (or equivalent) data and absolute timeinformation. The aiding information is transmitted to the GPS receiverusing some alternative form of communication (usually wireless, such ascellular data channels). Thanks to the use of GPS Aiding, GPS receiverscan operate in areas where signal levels are too low for traditional GPSto function properly.

All GPS Aiding, thus far invented, requires accurate external knowledgeof the absolute time, so that the satellite positions can be accuratelydetermined. The absolute time is required to an accuracy of between 1millisecond and 10 milliseconds. Unfortunately, there are desiredimplementations of GPS Aiding where absolute time cannot easily beobtained to this accuracy at the GPS receiver. For example: the AMPScellular phone system does not support time information; nor (currently)does the North American TDMA cellular phone system. The GSM cellularphone system supports timing information, but may have different timereferences in different geographical regions. In these situations it isdesirable to provide a method for computing GPS receiver positionwithout knowing the absolute time.

More specifically, Global Positioning System (GPS) receivers receive GPSsignals transmitted from orbiting GPS satellites containing uniquepseudo-random noise (PN) codes. The GPS receivers determine the timedelays between transmission and reception of the signals by comparingtime shifts between the received PN code signal sequence and internallygenerated PN signal sequences.

Each transmitted GPS signal is a direct sequence spread spectrum signal.The signals available for commercial use are provided by the StandardPositioning Service. These signals utilize a direct sequence spreadingsignal with a 1.023 MHz spread rate on a carrier at 1575.42 MHz (the L1frequency). Each satellite transmits a unique PN code (known as the C/Acode) that identifies the particular satellite, and allows signalstransmitted simultaneously from several satellites to be receivedsimultaneously by a receiver with very little interference of any onesignal by another. The PN code sequence length is 1023 chips,corresponding to a 1 millisecond time period. One cycle of 1023 chips iscalled a PN frame. Each received GPS signal is constructed from the1.023 MHz repetitive PN pattern of 1023 chips. At very low signal levelsthe PN pattern may still be observed, to provide unambiguous time delaymeasurements, by processing, and essentially averaging, many PN frames.These measured time delays are called “sub-millisecond pseudoranges”,since they are known modulo the 1 millisecond PN frame boundaries. Oncethe absolute time delay can be calculated, by resolving the integernumber of milliseconds associated with each delay to each satellite,then one has true, unambiguous, pseudoranges. The process of resolvingthe unambiguous pseudoranges is known as “integer millisecond ambiguityresolution”.

A set of four pseudoranges together with a knowledge of the absolutetimes of transmissions of the GPS signals and satellite positions atthose absolute times is sufficient to solve for the position of the GPSreceiver. The absolute times of transmission are broadcast from thesatellites in the Navigation Message, which is superimposed on the 1.023MHz PN code at a lower, 50 Hz, data rate. This 50 Hz signal is a binaryphase shift keyed (BPSK) data stream with bit boundaries aligned withthe beginning of the PN frame. There are exactly 20 PN frames per databit period (20 milliseconds). The 50 Hz signal contains data bitsdescribing the GPS satellite orbits, satellite clock corrections, timeof week information, and other system parameters.

The absolute times associated with the satellite transmissions aredetermined in conventional GPS receivers by reading the Time of Week(TOW) data in the Navigation Message of the GPS signal. In the standardmethod of time determination, a conventional GPS receiver decodes andsynchronizes to the 50 baud data stream. The 50 baud signal is arrangedinto 30-bit words grouped into subframes of 10 words, with a length of300 bits and a duration of six seconds. Five subframes comprise a frameof 1500 bits and a duration of 30 seconds, and 25 frames comprise asuperframe with a duration of 12.5 minutes. A superframe contains thecomplete Navigation Message. The data bit subframes that occur every sixseconds contain bits that provide the TOW to six second resolution. The50 baud data stream is aligned with the C/A code transitions so that thearrival time of a data bit edge (on a 20 ms interval) resolves theabsolute transmission time to the nearest 20 milliseconds. Precisionsynchronization to bit boundaries can resolve the absolute transmissiontime to one millisecond or less.

The absolute times associated with the satellite signals are determinedin Wireless Aided-GPS receivers by having an external timing source thatis calibrated to GPS time then using this time to provide a precise timetag at the time of reception of the satellite signal. The time ofreception minus the pseudorange gives the absolute time of transmissionfor each satellite (with the pseudorange expressed in time units,reflecting the transmission-reception time delay).

The absolute times of transmission are needed in order to determine thepositions of the satellites at the times of transmission and hence todetermine the position of the GPS receiver. GPS satellites move atapproximately 3.9 km/s, and thus the range of the satellite, observedfrom the earth, changes at a rate of at most ±800 m/s. Absolute timingerrors result in range errors of up to 0.8 m for each millisecond oftiming error. These range errors produce a similarly sized error in theGPS receiver position. Hence, absolute time accuracy of 10 ms issufficient for position accuracy of approximately 10 m. Absolute timingerrors of much more than 10 ms will result in large position errors, andso typical GPS receivers have required absolute time to approximately 10millisecond accuracy or better.

Note that absolute timing errors also introduce errors as a result ofthe GPS satellite clock drift, but these are so much smaller than thesatellite position error that they can be ignored for the purposes ofthis explanation (GPS clocks drift typically less than 0.1 nanosecondsper second, and the observed range to the satellite is affected by theGPS clock drift multiplied by the speed of light, this error is lessthan 0.03 m/s, about 25 thousand times smaller than errors caused bychanges in satellite position).

There is another time parameter closely associated with GPS positioning,this is the sub-millisecond offset in the time reference used to measurethe sub-millisecond pseudorange. This offset affects all themeasurements equally, and for this reason it is known as the “commonmode error”.

The common mode error should not be confused with the absolute timeerror. As discussed above, an absolute time error of 1 millisecond leadsto range errors of up to 0.8 meters while an absolute time error of 1microsecond would cause an almost unobservable range error of less than1 millimeter. However, a common mode error of 1 microsecond causes apseudorange error of 1 microsecond multiplied by the speed of light,that is 300 meters.

Because common mode errors have such a large effect on pseudoranges, andbecause it is practically very difficult to calibrate the common modeerror, traditional GPS receivers treat the common mode error as anunknown that must be solved for, along with position, once sufficientlymany pseudoranges have been measured at a particular receiver. However,no traditional GPS receivers solve for absolute time error insteadrelying on the fact that they know absolute time to the requiredaccuracy (of 10 milliseconds or better).

Therefore, a need exists in the art for a method and apparatus thatprocesses GPS signals without using absolute time.

SUMMARY OF THE INVENTION

The present invention is a method and apparatus for computing GPSreceiver position without using absolute time information transmitted bya satellite or by an alternative source of timing available at the GPSreceiver. In an embodiment of the invention, the GPS receiver iscontained in an integrated receiver that also includes a wirelesscommunication transceiver, but does not have access to an accuratesource of absolute time information. The wireless transceivercommunicates through a wireless network to a server. The GPS receivermeasures satellite pseudoranges and uses the wireless communicationtransceiver to send the pseudoranges to the server. The server fits thepseudoranges to a mathematical model in which the GPS receiver positionand the absolute time are unknown parameters. The server then computes aposition and absolute time that best fit the model, thus yielding thecorrect position for the GPS receiver, and the absolute time at whichthe pseudorange measurements were made.

BRIEF DESCRIPTION OF THE DRAWINGS

The teachings of the present invention can be readily understood byconsidering the following detailed description in conjunction with theaccompanying drawings, in which:

FIG. 1 depicts a block diagram of apparatus for computing a GPS receiverlocation without knowledge of absolute time;

FIG. 2 depicts a flow diagram representing the operation of theapparatus of FIG. 1;

FIG. 3 depicts a flow diagram representing a method of computingpseudoranges in accordance with the invention;

FIG. 4 depicts a flow diagram representing a method of computingreceiver position and absolute time in an alternative embodiment of theinvention;

FIGS. 5A and 5B graphically depict a grid (5A) used for producing theresidual magnitudes (5B) of position error; and

FIG. 6 depicts a graph of the residual time error used in computing anabsolute time.

To facilitate understanding, identical reference numerals have beenused, where possible, to designate identical elements that are common tothe figures.

DETAILED DESCRIPTION

The invention is a method and apparatus for determining position andtime in a global positioning system (GPS) without having access, at theGPS receiver, to absolute time information. In the followingdescription, for purposes of explanation, numerous specific details areset forth in order to provide a thorough understanding of the presentinvention. It will be evident, however, to one skilled in the art thatthe present invention may be practiced without these specific details.

FIG. 1 depicts one embodiment of the present invention comprising anintegrated mobile receiver 102 coupled to a server 121 via a wirelesslink 150. A GPS receiver 108 is contained in the integrated receiver 102along with a wireless communication transceiver 112. The GPS receiver108 measures only sub-millisecond pseudoranges with respect to GPSsatellites that are in view of the receiver 108, and then sends thesesub-millisecond pseudo-ranges to a server 121 using a wirelesscommunication link 150. The server 121 forms an approximate, a-prioriestimate of the GPS receiver position from the known location of awireless tower 118 used to receive the wireless communication. Theserver 121 also allocates a time tag from its own real time clock, thuscreating an a-priori estimate of the absolute time at which the GPSreceiver 108 received the GPS signals from the satellites. If thea-priori position is within 100 km of the true position, and thea-priori absolute time of reception is within one minute of the true(unknown) time of reception, then the server 121 can resolve the integermilliseconds, thus turning the sub-millisecond pseudoranges into truepseudoranges.

Next, the server 121 uses the pseudoranges to solve for the unknownreceiver position and absolute time. The server comprises a centralprocessing unit (CPU) 122, a server clock 124, a tower location database128, CPU support circuits 152, and memory 154. The support circuitscomprise well-known circuits that facilitate operation of the CPU suchas clock circuits, cache, power supplies, I/O interface circuits, andthe like. The memory 154 may be random access memory, read only memory,removable storage, hard disk storage, or any combination of these memorydevices.

In one embodiment of the invention, the common mode error is assumed tobe totally unknown at the server 121. In the one embodiment of theinvention, the server 121 assumes an a-priori common mode error of zero,although it will be understood that any other a-priori common mode errorcould be used, with no change in the results. With the five a-prioriestimates of the unknown parameters (3 coordinates of position, 1absolute time, 1 common mode error) the server 121 creates amathematical model relating the measured pseudoranges and a-prioriinformation to the unknown parameters. The mathematical model can bewritten as a linear equation, which, when solved, yields the correctposition and absolute time.

More specifically, GPS signals 104 from a plurality of satellites (notshown) are received at the GPS antenna 106. The received signals arecoupled to the GPS receiver 108. The GPS receiver 108 processes the GPSsignals to form sub-millisecond pseudoranges on path 110, which arecoupled to the communication transceiver 112 and transmitted from thecommunication antenna 116 through a wireless network such as a cellulartelephone network. The transmission from the integrated receiver 102 isreceived by a nearby radio tower 118, e.g., a cellular telephone tower.The sub-millisecond pseudoranges and the radio tower ID are sent fromsaid radio tower 118 to the server 121. In the server 121 the serverclock 124 is used to provide a time-tag when the sub-millisecondpseudoranges are received at the server. The server 121 passes the radiotower ID along path 126 to a tower location database 128, and extracts alocation for the tower from the database 128. The tower location iscoupled to the CPU 122 along path 130.

The satellite ephemeris data, for all satellites represented by thesub-millisecond pseudorange data, is provided to the server from someexternal source 125 (such as another GPS receiver located in thevicinity of the server with a clear view of the sky, or some othersource such as a network of GPS receivers). Note that, for simplicity,the term “ephemeris” is used to mean the satellite orbital parameters,as well as the satellite clock parameters. The CPU 122 of the server 121combines the sub-millisecond pseudoranges, radio tower location, servertime, and ephemeris to form the correct GPS receiver position andabsolute time of reception of signals at the GPS receiver 108.

The apparatus above assumes that the GPS receiver 108 is not capable ofreliably receiving the absolute time information and ephemeris data,i.e., the GPS receiver is used indoors, such that the processing ofephemeris data is accomplished in the server 121. However, in someinstances, rather than having the pseudo range data supplied to theserver, the server (or some other source) can supply the ephemeris dataand clock signal to the mobile device 102 and the mobile device canperform the position calculation. In such an embodiment of theinvention, a CPU and clock (similar to 122 and 124) are located in themobile device 102 to facilitate signal processing in the same manner asis described with respect to the server 121.

FIG. 2 is a flowchart illustration of the process 200 that is performedby the server CPU 122 of FIG. 1. At step 202, the server clock signal isused to provide an a-priori estimate of the absolute time of receptionof the GPS signals at the GPS receiver. It will be understood that theuse of the server clock is one embodiment used to exemplify the currentinvention and, in general, the a-priori estimate of time could come froma time source other than the server clock. The present invention isapplicable irrespective of the source, or quality, of the a-prioriestimate of absolute time. To simplify the exposition, this particularembodiment is assumed to have a server clock that provides a time tagwithin one minute of the actual absolute time of reception of the GPSsignals at the GPS receiver. It will be understood that this simplifyingassumption, while often true in practice, is not a necessary part of theinvention, and has been used here only to simplify the explanation ofthe invention. Later in this specification, this simplifying assumptionis removed.

At step 206, the tower location is provided to the CPU as an a-prioriestimate of the GPS receiver position. It will be understood that theuse of the tower location is just one embodiment of any number ofa-priori positions that could be used (for example: a previouslycalculated position for the same GPS receiver 108 could be used as ana-priori position, or a combination of positions of recently usedtowers, or the a-priori position could simply be guessed). The presentinvention is applicable irrespective of the source, or quality, of thata-priori position. To simplify the exposition, this particularembodiment is assumed to have an a-priori position that is within 100 kmof the true position of the GPS receiver 108. It will be understood thatthis simplifying assumption, while often true in practice, is not anecessary part of the invention, and has been used here only to simplifythe explanation of the invention. Later in this specification thissimplifying assumption is removed.

At step 204 and 208, the sub-millisecond pseudoranges and ephemeris forthe appropriate satellites that are in view of GPS receiver are alsoprovided as inputs to the process 200.

At step 210, the sub-millisecond pseudorange integers are resolved by aprocess described below with respect to FIG. 3. Having resolved thesub-millisecond pseudorange integers, the process creates fullpseudoranges.

At step 212, the expected pseudoranges are formed. These expectedpseudoranges are the pseudoranges that would be measured if all thea-priori parameters (a-priori position, a-priori absolute time ofmeasurement, and a-priori common mode error) were in fact the actualvalues of these parameters. The expected pseudoranges are denoted r_(i),the index i denotes the appropriate satellite.

At step 214, the a-priori pseudorange residuals are formed, theseresiduals are defined as the difference between the measuredpseudoranges (denoted ρ_(i)) and the expected pseudoranges (r_(i)). Thea-priori pseudorange residuals are denoted u_(i).

At step 216 a mathematical model is formed, relating u to x, where u isa vector of u_(i) and x is a vector of the updates to the a-priorivalues of position, common-mode error, and absolute time of reception:${\underset{\_}{u} = \begin{bmatrix}u_{1} \\u_{2} \\\vdots \\u_{n}\end{bmatrix}},$

where n is the number of pseudoranges. The pseudoranges are expressed inunits of length (e.g. meters). $\underset{\_}{x} = {\begin{bmatrix}x \\y \\z \\t_{C} \\t_{S}\end{bmatrix}.}$

The position updates, x, y, z, are expressed in units of length (e.g.meters) and the time updates t_(c), t_(s) are in units of time (e.g.seconds)

An embodiment of a mathematical model relating these two vectors is aTaylor series, where the first term in the series is the firstderivative of u with respect to x, the second term contains the secondderivative, and so on. In one embodiment of the process, the inventionuses a linearized model that keeps only the first derivative in theTaylor series. This gives the following equation relating u to x:$\begin{matrix}{\underset{\_}{u} = {\begin{bmatrix}u_{1} \\\quad \\u_{n}\end{bmatrix} = {\begin{bmatrix}{{\partial\rho_{1}}/{\partial x}} & {{\partial\rho_{1}}/{\partial y}} & {{\partial\rho_{1}}/{\partial z}} & {{\partial\rho_{1}}/{\partial t_{C}}} & {{\partial\rho_{1}}/{\partial t_{S}}} \\\vdots & \vdots & \vdots & \vdots & \vdots \\{{\partial\rho_{n}}/{\partial x}} & {{\partial\rho_{n}}/{\partial y}} & {{\partial\rho_{n}}/{\partial z}} & {{\partial\rho_{n}}/{\partial t_{C}}} & {{\partial\rho_{1}}/{\partial t_{S}}}\end{bmatrix}\begin{bmatrix}x \\y \\z \\t_{C} \\t_{S}\end{bmatrix}}}} \\{= {\begin{bmatrix}{{\partial\rho_{1}}/{\partial x}} & {{\partial\rho_{1}}/{\partial y}} & {{\partial\rho_{1}}/{\partial z}} & c & {- {\overset{.}{\rho}}_{1}} \\\vdots & \vdots & \vdots & \vdots & \vdots \\{{\partial\rho_{n}}/{\partial x}} & {{\partial\rho_{n}}/{\partial y}} & {{\partial\rho_{n}}/{\partial z}} & c & {- {\overset{.}{\rho}}_{n}}\end{bmatrix}\begin{bmatrix}x \\y \\z \\t_{C} \\t_{S}\end{bmatrix}}} \\{= {H\quad \underset{\_}{x}}}\end{matrix}$

The particular values of ∂ρ_(i)/∂x_(i) ∂ρ_(i)/∂y, and ∂ρ_(i)/∂z dependon the coordinate system used to describe the a-priori position. Theseterms in the first three columns of the matrix H are well known in theart, and further explanation is not required. The fourth column of thematrix is c, the speed of light, this part of the model is also standardin the art. The novel aspect of this invention requires the inclusion ofthe fifth column in the matrix. This fifth column exactly models therelationship between the unknown error in the a-priori estimate ofabsolute time, and the measured pseudoranges. Furthermore the terms inthis column are the rate of change of the pseudoranges with respect totime and can be exactly calculated from the ephemeris data. Hence everyterm in the matrix H is known and, provided there are five or morepseudoranges available at the GPS receiver, the values of x can becalculated using linear algebra.

At step 220, the GPS receiver position is computed by adding the updatesx,y,z, to the a-priori position, and the absolute time of reception isformed by adding the update t_(s) to the a-priori time of reception. Ifthe a-priori position and a-priori absolute time were close enough tothe true position and true absolute time, then one pass through theprocess 200 will yield results to the required accuracy. However, if thefirst pass through the process 200 does not immediately converge on therequired accuracy, then the result 222 is used to form a new a-prioritime of reception estimate for step 202 and a new a-priori positionestimate for step 206, and the process 200 is repeated until the resultconverges on the correct result (typically very few iterations arerequired because the linearization using the first order Taylor seriesis a very good mathematical description of the complete, non-linear,system, thanks to the fact that the satellite ranges are so much furtherfrom the earth than the error in the a-priori position). It will beunderstood that the Taylor series is just one example of a mathematicalmodel relating the unknown position and absolute time to the measuredpseudoranges. The present invention is equally valid with other models,such as non-linear models, which can be solved through techniques suchas iteratively fitting the unknown parameters until an acceptablesolution is obtained.

If, as assumed above, the a-priori position and a-priori absolute timeare within 100 km and 1 minute respectively, then the result 222 will becorrect. However, if the a-priori position and time are not known withinthese limits, then the incorrect integers may be formed at step 210 andthe incorrect result 222 may be obtained. In this case the a-posterioriresiduals, formed at step 224, will be used, as described below withrespect to FIG. 4, to detect this errant condition and then differenta-priori values will be used.

FIG. 3 is a flowchart of an illustrative process 300 that resolves thesub-millisecond pseudorange integers (step 210 of FIG. 2). To simplifythe exposition, this particular embodiment is assumed to have ana-priori position that is within 100 km of the true position of the GPSreceiver, and an a-priori absolute time estimate that is within oneminute of the true absolute time of reception at the GPS receiver. Itwill be understood that these simplifying assumptions, while often truein practice, are not a necessary part of the invention, and have beenused here only to simplify the explanation of this embodiment of theinvention. In the description relating to FIG. 4, FIG. 5, and FIG. 6,these simplifying assumptions are removed.

At step 308, the process 300 calculates the expected pseudoranges usingephemeris data (provided in step 208) for the satellites along with thea-priori absolute time of reception (provided in step 202) and thea-priori position (provided in step 206). As done throughout thisspecification, the term ephemeris is used to mean the satellite orbitalparameters as well as the satellite clock parameters.

At step 310, a single satellite is chosen as a reference satellite. Inthe preferred embodiment the satellite with the highest elevation angle(from the a-priori position) is chosen as the reference, but it will beunderstood that it is not important which satellite is used as thereference. The expected pseudorange for the reference satellite isdenoted r₀ (path 312). The expected pseudoranges for the othersatellites are denoted r_(i) (path 314).

At step 318, an integer is assigned to the reference satellite. Theinteger must satisfy the equation:

N ₀ *c/10³ +s ₀ t _(C) =r ₀ −e ₀,

where c is the speed of light, expressed in m/s, t_(c) is the commonmode error, and e₀ is the error in the expected pseudorange introducedby the combined errors in the a-priori position and a-priori absolutetime.

Those skilled in the art will understand that an arbitrary integer maybe assigned, since in the following discussion it is seen that thecommon mode error will absorb any errors made in this integer, as longas exactly equal errors are made in all the other integers. The integerN₀ is assigned according to the following equation:

N ₀=round ((r ₀ −s ₀)*10³ /c).

At step 322, the integer millisecond values for the remaining satellitesare calculated using the sub-millisecond pseudoranges 320 for all thesatellites along with N₀. Whatever value of N₀ was chosen above impliesan associated common mode error t_(c). The values of N_(i) are chosen tosatisfy the following equation, which relates N_(i), the measuredsub-millisecond pseudorange (s_(i)), the expected pseudorange (r_(i)),and the common mode error (t_(c))

N ₀ *c/10³ +s _(i) −t _(C) =r _(i) −e _(i),

where, e_(i) is the error in the expected pseudorange introduced by thecombined errors in the a-priori position and a-priori absolute time. Inthe preferred approach, the corresponding equation for N₀ is subtractedfrom the above equation, this exactly cancels the term t_(c), since thisterm is common (by definition) for all satellites. This yields thefollowing expression for N_(i)

N _(i)=round(N ₀(s ₀ −s _(i) +r _(t) −r ₀)*10³ /c).

The above equations represent one embodiment of a process to calculatethe integers. It will be understood that any expression may be used tocompute these integers, provided the relationship to t_(c) isconsistently maintained for all the integers.

In the above description the assumption was made that the a-prioriposition was within 100 km of the true position, and the a-prioriabsolute time was within 1 minute of the true time. For all GPSsatellites, the maximum pseudorange rate is ±800 m/s. Thus the maximumvalue of the error term e_(i) will be 100 km+60s*0.8 km/s=148 km. Thisis less than half of one C/A code millisecond epoch (i.e., less thanhalf of one integer millisecond) and the rounding operation used abovewill always yield the correct integers. In the disclosure with respectto FIG. 4, FIG. 5, FIG. 6, these two restrictions on a-priori positionaccuracy and a-priori time accuracy are removed.

If the a-priori position is not known to within 100 km, it willnonetheless be known to some finite accuracy limit. Similarly, if thea-priori absolute time is not known to within 1 minute it will benonetheless be known to some finite accuracy limit. As described in theprocesses 200 and 300, any a-priori position and time estimate withinthe 100 km and 1 minute constraints will yield the correct integers,correct GPS receiver position, and correct absolute time. In anembodiment of the current invention, the space of all possible a-prioripositions is divided into a 100 km×100 km lat-lon grid, with altitudeassigned from a look-up table of topographical altitudes. Similarly thespace of all possible a-priori absolute times is divided into 1-minutesegments. This yields a set of all possible a-priori positions andtimes. The process 200 is used iteratively, with each of the possiblea-priori position and time values from the set. When an a-prioriposition and time is found within 100 km and 1 minute of truth, then thea-posteriori residuals will be small, and the correct GPS receiverposition and absolute time will be computed, as described above.

An embodiment of this process 400 is shown in FIG. 4. At step 402, allpossible a-priori positions and residuals are formed into a set. In oneembodiment the set is organized as a 100 km×100 km grid, with altitudesassigned from a lookup table of topographical heights, and with timesegmented into 1-minute segments. This is a convenient representationbecause, as discussed above, the combination of a 100 km grid plus themaximum pseudorange rate times 1-minute gives a maximum possibleestimated error of just less than half a millisecond of range, which isnecessary for the integer resolution process 300 to select the correctintegers. However it will be understood that any number of differentmethods may be used to organize the set of all possible a-priori values,including creating new elements of the set dynamically, based on theresults obtained from previously used values.

At step 404, the process 400 selects one possible a-priori position andtime combination. These values are used in the process 200. At step 406,the process 400 examines the a-posteriori residuals that are produced instep 224 of FIG. 2. If the correct GPS receiver position and absolutetime have been calculated, then the magnitude of the residuals will besmall (that is, of the same order as the pseudorange measurementerrors—tens of meters). If the a-priori position and time were farenough away from the truth that the integer ambiguities were notcorrectly resolved, then the residuals will be large (that is, of theorder of one millisecond epoch—many kilometers). If the residuals arelarge then the candidate a-priori position and time are incorrect andthey are removed from the set of possibilities. The process 400 isiterated until the correct position and absolute time are calculated.

It will be understood by those skilled in the art that even if theabsolute time is available at the GPS receiver, the process of integerambiguity resolution has traditionally required an initial estimate ofposition close enough to the true position for the integers to beuniquely defined by said initial estimate. The current inventionprovides a novel means of computing the correct integers withoutrequiring an accurate initial estimate of position.

FIGS. 5A and 5B respectively depict a grid 502 used to determinereceiver position in an embodiment of the invention and the residualmagnitudes 506 computed during the position calculation process 200. Inthis example, the a-priori position is assigned as an arbitrary guess,in the middle of North America. Then the process 200 is performed foreach possible a-priori position (grid point 504), and the magnitude ofthe a-posteriori residuals is examined. As each wrong candidate isrejected another candidate (another grid point 504) is generated bysearching outwards on a 1 degree×1 degree grid 502. (Note that this 1degree×1 degree grid is a slightly different embodiment than the 100 km×100 km grid described earlier; both embodiments are guaranteed to giveat least one a-priori position that will yield the correct integers, andhence the correct position and absolute time.) The a-priori position iscompleted by assigning an a-priori altitude from a lookup table oftopographical heights. FIG. 5A shows the 1,663 wrong candidates on agrid 504 and FIG. 5B shows the corresponding residual magnitudes 506,each one of the order of an incorrect millisecond integer (i.e., manykilometers). Once the search reaches an a-priori position in thevicinity of the true position (in San Jose, Calif.) the mathematicalmodel causes the correct result to “snap” into place, and the correctposition and time are calculated. The a-priori position candidate number1,664 (residual magnitude 508 and grid point 510) is approximately 175km east of the true position, which, in this example is close enough forthe position and time solution to “snap” into place. The correctsolution yields a residual that is approximately 30 meters, which isfrom one thousand to ten thousand times smaller than the incorrectresiduals.

The large difference between “small” residuals (tens of meters) and“large” residuals (tens to hundreds of kilometers) makes this embodimentwork very well in practice. However, it will be understood that othermethods may be used to test the quality of the result, includingcomparing the calculated position and absolute time to a position andtime obtained through some other means—such as the location of the radiotower used in a wireless-aided system. It will also be appreciated thatin order to have non-zero residuals, it is necessary to have moreindependent observations than unknowns. In the embodiments describedthus far, there have been five unknown parameters: three coordinates ofposition, common mode error, and absolute time. Thus at least sixindependent measurements are required to have non-zero residuals. If sixGPS satellites can be observed, then the six measurements can beobtained from them. If there are not six satellites observable thenthere are several steps that can be taken, many of which are standard inthe art. The number of measurements may be increased by includingmeasurements from other sources (such as range measurements based ontime-of-arrival from a wireless system, or angle-of-arrival measurementsmeasured in a wireless system, or any other independent measurement thatcan be obtained).

The number of observables can also be increased by including, as“pseudo-measurements”, known constraints on position, for example knownor approximately known altitude can be introduced into the mathematicalmodel as a pseudo-measurement. In the embodiment specified above, wherethe mathematical model is represented by the equation u=Hx, apseudo-measurement for known altitude may be created by first specifyingthe a-priori position in coordinates of latitude, longitude, andaltitude, then by setting the a-priori altitude to the known altitude,then by adding a new line to the matrix equation: $\begin{bmatrix}\underset{\_}{u} \\0\end{bmatrix} = {\begin{bmatrix}\quad & \quad & H & \quad & \quad \\0 & 0 & 1 & 0 & 0\end{bmatrix}\quad {\underset{\_}{x}.}}$

This approach effectively adds another measurement or observable to themathematical model. This approach is standard in the art, and it isunderstood that it applies to any constraints that may be useful insolving for the unknown parameters.

Another approach is to reduce the number of unknown parameters. This maybe performed by removing known, or approximately known parameters. Themost commonly known parameter is altitude, and it can be removed fromthe mathematical model. Similarly the common mode error may becalibrated (for example, if the invention is implemented in a systemwith access to a stable oscillator) and removed from the mathematicalmodel.

It will be appreciated that many combinations of the disclosedtechniques may be applied to compute unknown values, including unknownabsolute time.

For example, using the techniques of this invention, one can compute thetime parameters alone, without computing the position. This is done, inthe preferred embodiment, by fixing the position in the mathematicalmodel to the a-priori position, and computing the remaining two unknownparameters: common mode error and absolute time.

FIG. 6. is a graphical representation 600 of the residuals magnitudes(axis 602) associated with the different a-priori times (axis 604) thatwere attempted in an example embodiment of the invention. In thisparticular example, a range of possible times, each one-minute apart, isattempted for each of the grid points shown in FIG. 5. The firsta-priori absolute time was chosen by guessing a time that turns out tobe approximately two-and-a-half hours later than the true absolute timeof reception. When the process 400 applies an a-priori positionapproximately 175 km away from the true position, and an a-priori timewithin one minute of the true absolute time, the mathematical modelcalculates the correct position and time, as shown in FIG. 5. Ingeneral, the mathematical model will calculate the correct position andtime as soon as the a-priori position and time are close enough to causeprocess 300 to calculate the correct integers. As discussed, thepreferred embodiment is guaranteed to find at least one such a-prioriposition and time, by creating an appropriate grid, and appropriatelyspaced time intervals.

Although the methods and apparatus of the present invention have beendescribed with reference to GPS satellites, it will be appreciated thatthe teachings are equally applicable to positioning systems whichutilize pseudolites or a combination of satellites and pseudolites.Pseudolites are ground based transmitters that broadcast a PN code(similar to the GPS signal) which may be modulated on an L-band carriersignal, generally synchronized with GPS time the term “satellite”, asused herein, is intended to include pseudolites or equivalents ofpseudolites, and the term “GPS signals”, as used herein, is intended toinclude GPS-like signals from pseudolites or equivalents of pseudolites.

In the preceding discussion the invention has been described withreference to application upon the United States Global PositioningSystem (GPS). It should be evident, however, that these methods areequally applicable to similar satellite systems, and in particular, theRussian Glonass system and the European Galileo system. The term “GPS”used herein includes such alternative satellite positioning systems,including the Russian Glonass system and the European Galileo system.

Although various embodiments which incorporate the teachings of thepresent invention have been shown and described in detail herein, thoseskilled in the art can readily devise many other varied embodiments thatstill incorporate these teachings.

What is claimed is:
 1. A method for calculating an absolute position ofa GPS receiver and an absolute time of reception of satellite signalscomprising: providing pseudoranges that estimate the range of the GPSreceiver to a plurality of GPS satellites; providing an estimate of anabsolute time of reception of a plurality of satellite signals;providing an estimate of a position of the GPS receiver; providingsatellite ephemeris data; computing absolute position and absolute timeusing said pseudoranges by updating said estimate of an absolute timeand the estimate of position of the GPS receiver.
 2. The method oc claim1 wherein said pseudoreanges are sub-millisecond pseudoranges.
 3. Themethod of claim 1, wherein a first instance of said estimate of absolutetime is in error by more than 10 milliseconds.
 4. The method of claim 1,wherein said estimate of absolute time is provided by a clock that isnot linked to a GPS reference time.
 5. The method of claim 1, whereinsaid estimates of position and absolute time may be arbitrary guesses.6. The method of claim 1, further comprising: forming a-prioripseudorange-residuals; and forming a mathematical model relating saida-priori pseudorange-residuals to said updates of said position andabsolute time estimates; and computing updates of the position andabsolute time that fit the mathematical model.
 7. The method of claim 6,wherein said a-priori range-residuals are a difference between expectedranges, from said satellites to said a-priori position estimate, and thepseudoranges.
 8. The method of claim 6, wherein said expected ranges arecomputed at a time given by said a priori time estimate.
 9. The methodof claim 6, wherein said mathematical model is a linearization of aTaylor series of a non-linear mathematical model.
 10. The method ofclaim 9, wherein said linearization is of the form: u _(i)=[∂ρ_(i) /∂x,∂ρ _(i) /∂y, ∂ρ _(i) /∂z, ∂ρ _(i) /∂t _(C) , ∂ρ _(i) /∂t _(S) ]*[x, y,z, t _(C) , t _(S)]^(T) where: u_(i) is the a-priori range-residual, forone satellite; ρ_(i) is the pseudorange for a satellite i; x, y and zare three coordinates of position updates; t_(C) is a common mode errorupdate; t_(S) is an absolute time of reception update; and ∂ adenotesthe partial derivative.
 11. The method of claim 4, wherein one or moreof the updates is assumed known, so that the remaining updates may becomputed.
 12. The method of claim 10, wherein one or more of the updatesx, y, z, or t_(C) is assumed known, and set equal to an assumed value inthe mathematical model, so that the remaining updates may be computed.13. The method of claim 10, wherein one or more of the updates x, y, z,or t_(C) is assumed known, and added to the model as apseudo-measurement so that the remaining updates may be computed.
 14. Aprocess as in claim 6, wherein other measurements or constraints areused in the mathematical model.
 15. A process as in claim 6, whereinsaid a-priori position is obtained from a location of a radio tower usedto communicate with a mobile device containing said GPS receiver.
 16. Aprocess as in claim 6, wherein said absolute time estimate is obtainedfrom a real time clock in a server, said server being located remotelyfrom said GPS receiver.
 17. A method for calculating absolute time ofreception of satellite signals in a GPS receiver comprising: providingpseudoranges that estimate the range of the GPS receiver to a pluarlityof GPS satellites; providing an estimate of position of the GPSreceiver; and computing absolute time using the pseudoranges and theposition estimate.
 18. The method of claim 1 wherein said pseudorangesare sub-millisecond pseudoranges.
 19. The method of claim 17, furthercomprising: forming a-priori pseudorange-residuals; and forming amathematical model relating said a-priori pseudorange-residuals toupdates of said estimate of position and absolute time; and computingupdates of the position and absolute time that fit the mathematicalmodel.
 20. The method of claim 19, wherein said a-priori range-residualsare a difference between expected ranges, from said satellites to saida-priori position estimate, and the pseudoranges.
 21. The method ofclaim 19, wherein said expected ranges are computed at a time given bysaid a priori time estimate.
 22. The method of claim 19, wherein saidmathematical model is a linearization of a Taylor series of a non-linearmathematical model.
 23. The method of claim 22, wherein saidlinearization is of the form: u _(i) =[∂ρ _(i) /∂x, ∂ρ _(i) /∂y, ∂ρ _(i)/∂z, ∂ρ _(i) /∂t _(C) , ∂ρ _(i) /∂t _(S) ]*[x, y, z, t _(C) , t_(S)]^(T) where: u_(i) is the a-priori range-residual, for onesatellite; ρ_(i) is the pseudorange for a satellite i; x, y and z arethree coordinates of position updates; t_(C) is a common mode errorupdate; t_(S) is an absolute time of reception update; and ∂ denotes thepartial derivative.
 24. The method of claim 23, wherein one or more ofthe updates x, y, z, or t_(C) is assumed known, and set equal to anassumed value in the mathematical model, so that the remaining updatesmay be computed.
 25. The method of claim 24, wherein one or more of theupdates x, y, z, or t_(C) is assumed known, and added to the model as apseudo-measurement so that the remaining updates may be computed.
 26. Aprocess as in claim 24, wherein other measurements or constraints areused in the mathematical model.
 27. A process as in claim 24, whereinsaid a-priori position is obtained from a location of a radio tower usedto communicate with a mobile device containing said GPS receiver.
 28. Amethod of calculating a GPS position for a GPS receiver from partialpseudoranges that have ambiguity in a number of integer milliseconds,comprising: a) choosing an a-priori position of the GPS receiver; b)calculating integers conforming to said a-priori position; c)calculating a navigation solution; d) calculating a-posterioriresiduals; and e) using a relative size of said a-posteriori residualsto determine if said calculated integers are correct; and f) repeatingsteps c), d) and e) using another a-priori position until residualshaving a magnitude below a predefined threshold are computed.
 29. Amethod as in claim 28, wherein said a-priori position is not within aspecified distance of the actual receiver position.
 30. A method as inclaim 28, wherein said a-priori position is greater than 100 km from theactual receiver position.
 31. A method as in claim 28, wherein saida-priori position is greater than one integer millisecond from theactual receiver position.
 32. A method as in claim 28, wherein saida-priori position is an arbitrary guess.
 33. A system for computing anabsolute position of a GPS receiver and an absolute time of reception ofsatellite signals comprising: a mobile device comprising a GPS receiverand a wireless transceiver; a server being in wireless communicationwith said mobile device; where said GPS receiver computes pseudorangesthat estimate the range of the GPS receiver to a plurality of GPSsatellites and the wireless transceiver transmits said pseudoranges tothe server; where the server computes an absolute position and absolutetime for the GPS receiver using the pseudoranges and an estimate ofposition and time.
 34. The system of claim 33 wherein said pseudorangesare sub-millisecond pseudoranges.
 35. The system of claim 33 wherein theposition estimate is a position of a radio tower coupled to the serverthat receives signals from the wireless transceiver.